In the hall of fame of improbable headlines – think "Fifty Shades of Grey wins Booker" – let's nominate two more: "Romney crushes Obama"; and "British press hails Ed Miliband's presentational skills". Last weekend, to have dreamed of either eventuality, let alone both, would have sounded utterly delusional. Yet such is the magic of politics, here we are a week later and those dreams have come true. (Not, alas, for EL James, though there's always next year.)

Mitt Romney gave Barack Obama such a good hiding in their first TV debate, you half expected the referee to step in and end the bout on compassionate grounds. While the president was lethargic and passive, his talking points lost in a haze of numbers and Beltway detail, Romney fizzed, consistently crisp and direct. An instant poll of viewers gave it to the challenger by 67% to 25%, the first candidate to clear 60% since such post-debate surveys began in 1984.

Ed Miliband, meanwhile, won near-universal raves for a conference performance that stunned both his audience and a press corps that had come to believe the Labour leader could not perform his way out of a paper bag. Strong in the areas he had been deemed weak – in delivery and stage presence – he was showered in Twitter love, even by those Tory commentators who have made a living mocking him as Wallace's dweebier and nerdier twin. I understand that Tony Blair himself sent his successor a "lovely note". The amazing truth is that on the day, judged purely on the business of political communication, Miliband was better than Barack Obama. (Make that the week's third unlikely headline.)

The result is that the two incumbents on either side of the Atlantic are now on the back foot, under pressure to hit back soon, the demand especially intense from their own supporters. On Wednesday, Conservatives expect to see David Cameron remind them why they picked him seven years ago, delivering a conference spectacular that puts Miliband back in his place. Democrats yearn for Obama to mete out a similar pummelling to Romney six days later, at the second of their three head-to-head encounters.

The pressure on Obama is more urgent – Americans vote exactly one month tomorrow – while Cameron's date with the electorate is not till 2015. But the PM will be watching closely, mindful that occupants of high office in the age of austerity have much in common – little of it good.

Until now, Conservatives have watched Obama push ahead of Romney and comforted themselves that governments can defeat oppositions, even amid the economic gloom, so long as they move early and often to cast the challenger as extreme, unable to grasp the nature of the nation's core problem and drawn from the party that created that problem in the first place. What Obama had done to Romney, Cameron would do to Miliband. Throw in a charisma advantage over the challenger – who could be painted as stiff, wooden and a little weird – along with a plea for understanding from the electorate that results take time, and Obama seemed to have drawn a roadmap that could lead fellow incumbents, in Britain and beyond, to victory.

The Denver debate has shaken that complacency. For it showed that those tactics alone are not enough. A politician in power who wants to stay in power has to have what political operatives call a "forward offer". He can't simply trash his rival or defend his record. He has to talk about the future, about what he will do next.

This, rather than his infuriating, head-down failure to make eye contact with either the camera or his opponent, was what undid Obama on Wednesday night. He was raking over the events of the last four years, not sketching a vision of the next four. In this he was forgetting a lesson he had already learned. A year ago, Obama's message was that he had made a good start in getting "the car out of the ditch" and that he ought to be allowed to finish the job. Too backward-looking, says US pollster Stan Greenberg, onetime adviser to Bill Clinton and now helping Miliband. In a Manchester cafe thronging with Labour delegates this week, he told me that if the president had persisted with that theme, "he'd have lost". Fortunately Obama shifted, focusing instead on his plan for the future. As soon as he did, the numbers moved his way.

Cameron has to make the same move, starting on Sunday in Birmingham. He has to explain what the country will look like, once we emerge from the current economic trauma. Leaders always need to explain where they are leading, but that's doubly true in recession. Margaret Thatcher remained on top even during the hard times because she told the nation a story about why the medicine was painful and how much healthier we'd be once we'd swallowed it. People can endure all kinds of hardship if they know and accept why they're doing it. For all his oratorical skills, Obama has not constructed a similarly compelling narrative and nor has Cameron.

But it's harder for the PM. For one thing, there's the question of motive. One luminary of the right sighs that while voters often accuse parties of the centre-left of being "weak", they never think of them as "evil": "They assume their heart is in the right place." Even among those Americans who don't rate Obama, most believe he means well. The Conservatives enjoy no such starting assumption of benign intent (though Cameron himself once did).

Second, Cameron arrives in Birmingham on the defensive because Miliband has just placed his tanks on the Tory lawn, claiming for Labour the Disraelian mantle of one nation. "Cameron cannot afford to concede that ground," says one former Tory strategist. "He must contest it, contest it, contest it." In both Britain and the US, and this is surely what Labour has learned watching Obama, whoever can speak most convincingly for the many, not the few, whoever can own "we're all in this together" – to use two recent formulations of the same idea – will prevail. Which is why Romney's writing off of 47% of Americans was so disastrous – and why it is astonishing Obama did not mention it in Denver.

The president can turn things around with one good debate performance. Today he received a handy boost, as unemployment fell below the electorally critical 8% threshold for the first time since he took office in January 2009. Obama remains a blessedly lucky candidate. For Cameron, it will not be so easy.